Vibrations of a Cylindrical Sandwich Shell with a Honeycomb Core Made Using FDM technology

image_print
DOI https://doi.org/10.15407/pmach2021.04.049
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Pidhornyi Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN  2709-2984 (Print), 2709-2992 (Online)
Issue Vol. 24, no. 4, 2021 (December)
Pages 49-60
Cited by J. of Mech. Eng., 2021, vol. 24, no. 4, pp. 49-60

 

Authors

Borys V. Uspenskyi, A. Pidhornyi Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi str., Kharkiv, 61046, Ukrainе), e-mail: Uspensky.kubes@gmail.com, ORCID: 0000-0001-6360-7430

Kostiantyn V. Avramov, A. Pidhornyi Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi str., Kharkiv, 61046, Ukrainе), e-mail: kvavramov@gmail.com, ORCID: 0000-0002-8740-693X

Ihor I. Derevianko, Yuzhnoye State Design Office (3, Krivorizka str, Dnipro, 49008, Ukraine), A. Pidhornyi Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi str., Kharkiv, 61046, Ukrainе), e-mail: dereviankoii2406@gmail.com, ORCID: 0000-0002-1477-3173

 

Abstract

Presented is a model of the dynamic deformation of a three-layer cylindrical shell with a honeycomb core, manufactured by fused deposition modeling (FDM), and skins reinforced with oriented carbon nano-tubes (CNT). A ULTEM 9085 thermoplastic-based honeycomb core is considered. To analyze the stress-strain state of the honeycomb core, a finite element homogenization procedure was used. As a result of this procedure, the dynamic response of the honeycomb core is modeled by a homogeneous orthotropic material, whose mechanical properties correspond to those of the core. The proposed model is based on the high-order theory, extended for the analysis of sandwich structures. The skin displacement projections are expanded along the transverse coordinate up to quadratic terms. The honeycomb core displacement projections are expanded along the transverse coordinate up to cubic terms. To ensure the integrity of the structure, shell displacement continuity conditions at the junction of the layers are used. The investigation of linear vibrations of the shell is carried out using the Rayleigh-Ritz method. For its application, the potential and kinetic energies of the structure are derived. Considered are the natural frequencies and modes of vibrations of a one-side clamped cylindrical sandwich shell. The dependence of the forms and frequencies of vibrations on the honeycomb core thickness and the direction of reinforcement of the shell skins have been investigated. It was found that the eigenforms of a sandwich shell are characterized by a smaller number of waves in the circumferential direction, as well as a much earlier appearance of axisymmetric forms. This means that when analyzing the resonant vibrations of a sandwich shell, it is necessary to take into account axisymmetric shapes. Changing the direction of reinforcement of the skins with CNTs makes it possible to significantly influence the frequencies of the natural vibrations of the shell, which are characterized by a nonzero number of waves in the circumferential direction. It was found that this parameter does not affect the frequencies of the axisymmetric shapes of the shell under consideration.

 

Keywords: cylindrical sandwich shell, additive technologies, honeycomb core, nano-composite skin, eigenforms, axisymmetric vibration mode

 

Full text: Download in PDF

 

References

  1. Sahu, N. K., Biswal, D. K., Joseph, S. V, & Mohanty, S. C. (2020). Vibration and damping analysis of doubly curved viscoelastic-FGM sandwich shell structures using FOSDT. Structures, vol. 26, pp. 24–38. https://doi.org/10.1016/j.istruc.2020.04.007.
  2. Quyen, N. V., Thanh, N. V., Quan, T. Q., & Duc, N. D. (2021). Nonlinear forced vibration of sandwich cylindrical panel with negative Poisson’s ratio auxetic honeycombs core and CNTRC face sheets. Thin-Walled Structures, vol. 162, paper 107571. https://doi.org/10.1016/j.tws.2021.107571.
  3. Singha, T. D., Rout, M., Bandyopadhyay, T., & Karmakar, A. (2021). Free vibration of rotating pretwisted FG-GRC sandwich conical shells in thermal environment using HSDT. Composite Structures, vol. 257, paper 113144. https://doi.org/10.1016/j.compstruct.2020.113144.
  4. Bacciocchi, M. & Tarantino, A. M. (2020). Critical buckling load of honeycomb sandwich panels reinforced by threephase orthotropic skins enhanced by carbon nanotubes. Composite Structures, vol. 237, paper 111904. https://doi.org/10.1016/j.compstruct.2020.111904.
  5. Li, Y., Yao, W., & Wang, T. (2020). Free flexural vibration of thin-walled honeycomb sandwich cylindrical shells. Thin–Walled Structures, vol. 157, paper 107032. https://doi.org/10.1016/j.tws.2020.107032.
  6. Duc, N. D., Seung-Eock, K., Tuan, N. D., Tran, P., & Khoa, N. D. (2017). New approach to study nonlinear dynamic response and vibration of sandwich composite cylindrical panels with auxetic honeycomb core layer. Aerospace Science and Technology, vol. 70, pp. 396–404. https://doi.org/10.1016/j.ast.2017.08.023.
  7. Eipakchi, H. & Nasrekani, F. M. (2020). Vibrational behavior of composite cylindrical shells with auxetic honeycombs core layer subjected to a moving pressure. Composite Structures, vol. 254, paper 112847. https://doi.org/10.1016/j.compstruct.2020.112847.
  8. Nath, J. K. & Das, T. (2019). Static and free vibration analysis of multilayered functionally graded shells and plates using an efficient zigzag theory. Mechanics of Advanced Materials and Structures, vol. 26, pp. 770–788. https://doi.org/10.1080/15376494.2017.1410915.
  9. Chehreghani, M., Pazhooh, M. D., & Shakeri, M. (2019). Vibration analysis of a fluid conveying sandwich cylindrical shell with a soft core. Composite Structures, vol. 230, paper 111470. https://doi.org/10.1016/j.compstruct.2019.111470.
  10. Yang, C., Jin, G., Liu, Z., Wang, X., & Miao, X. (2015). Vibration and damping analysis of thick sandwich cylindrical shells with a viscoelastic core under arbitrary boundary conditions. International Journal of Mechanical Sciences, vol. 92, pp. 162–177. https://doi.org/10.1016/j.ijmecsci.2014.12.003.
  11. Karakoti, A., Pandey, S., & Kar, V. R. (2020). Free vibration response of P-FGM and S-FGM sandwich shell panels: A comparison. Materials Today: Proceedings, vol. 28, part 3, pp. 1701–1705. https://doi.org/10.1016/j.matpr.2020.05.131.
  12. Ramian, A., Jafari-Talookolaei, R.-A., Valvo, P. S., & Abedi, M. (2020). Free vibration analysis of sandwich plates with compressible core in contact with fluid. Thin–Walled Structures, vol. 157, paper 107088. https://doi.org/10.1016/j.tws.2020.107088.
  13. Uspenskiy, B., Avramov, K., Derevyanko, I., & Biblik, I. (2021). K raschetu mekhanicheskikh kharakteristik sotovykh zapolniteley, izgotovlennykh additivnymi tekhnologiyami FDM [Calculation of mechanical characteristics of honeycomb cores made by additive FDM technologies]. Aviatsionno-kosmicheskaya tekhnika i tekhnologiyaAerospace Engineering and Technology, no. 1, pp. 14–20 (in Russian). https://doi.org/10.32620/aktt.2021.1.02.
  14. Avramov, K. V., Uspenskyi, B. V., & Derevianko, I. I. (2021). Analytical calculation of the mechanical properties of honeycombs printed using the FDM additive manufacturing technology. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, 2021, vol. 24, no. 2, pp. 16–23. https://doi.org/10.15407/pmach2021.02.016.
  15. Shen, H. S. (2009). Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Composite Structures, vol. 91, iss. 1, pp. 9–19. https://doi.org/10.1016/j.compstruct.2009.04.026.
  16. Wang, Q., Qin, B., Shi, D., & Liang, Q. (2017). A semi-analytical method for vibration analysis of functionally graded carbon nanotube reinforced composite doubly-curved panels and shells of revolution. Composite Structures, vol. 174, pp. 87–109. https://doi.org/10.1016/j.compstruct.2017.04.038.
  17. Wang, Q., Cui, X., Qin, B., & Liang, Q. (2017). Vibration analysis of the functionally graded carbon nanotube reinforced composite shallow shells with arbitrary boundary conditions. Composite Structures, vol. 182, pp. 364–379. https://doi.org/10.1016/j.compstruct.2017.09.043.
  18. Amabili, M. & Reddy, J. N. (2010). A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells. International Journal of Non-Linear Mechanics, vol. 45, iss. 4, pp. 409–418. https://doi.org/10.1016/j.ijnonlinmec.2009.12.013.
  19. Derevianko, I., Avramov, K., Uspenskyi, B., & Salenko, A. (2021). Eksperymentalnyi analiz mekhanichnykh kharakterystyk detalei raket-nosiiv, vyhotovlenykh za dopomohoiu FDM adytyvnykh tekhnolohii [Experimental analysis of the mechanical characteristics of the components of the carrier rockets, prepared with the help of FDM additive technologies]. Tekhnichna mekhanika Technical Mechanics, no. 1, pp. 92–100. https://doi.org/10.15407/itm2021.01.092.
  20. Duc, N. D., Cong, P. H., Tuan, N, D, Tran, P., & Thanh, N. V. (2017). Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations. Thin–Walled Structures, vol. 115, pp. 300–310. https://doi.org/10.1016/j.tws.2017.02.016.

 

Received 13 October 2021

Published 30 December 2021